by Warren D. Smith, Dec. 2007. Skip to conclusion. (Executive summary)
IRV advocate Rob Richie recently hailed the Australian house elections (held 24 November 2007) as a "big success" for Instant Runoff Voting (IRV). These elections threw out both Prime Minister John W. Howard and his party, the NatLibs, enthroning Kevin Rudd and giving his Labour Party majority control.
|Party||Top-rank votes||%votes||#seats won|
|Lib/Nat||4546534+682424=5228958||32.10||55+10=65 (one was disputed)|
|Other third parties||246792+89810+222004||6.50||0|
|Unaffiliated||276369||2.23||2 (both former major-party members)|
But was this really a big success for IRV? We'll examine that here using data from the Australian Electoral Commission web site. (Warning: All this is based on data we got from the AEC on 30 November 2007, which was not in final form. However, it turned out the same seat counts ultimately arose, in the final say, as we tabulated.) The conclusions of that examination are as follows:
But that whole conclusion and gripe can be avoided, but the way out involves admitting that there was a different pathology ("failure to elect Condorcet winner") which occurred even more frequently. In each case where this alternate pathology occurred, the Green loser would have the following valid gripe, enabling them to attack the legitimacy of IRV:
∴ This IRV election system and my defeat are both bogus!
Note: there is a 2-way choice here – at least one of these two pathologies (and hence gripes) is valid in each election, but the incomplete data released by the AEC is insufficient to tell which. I suspect, however, that the second problem (the Green gripe) is the one that is correct in the vast majority of cases.
There were by our count exactly 9 races (of the 150 total races) where the plurality and IRV winners disagreed. (You can re-examine the 150 races here: http://vtr.aec.gov.au/HouseDivisionMenu-13745-NAT.htm. We initially counted 8 but Malcolm MacKerras pointed out there were actually 9 such races and we have now added the 9th: Bass.) In all 9 cases, the Labour candidate did not win the "plurality election" (IRV round #1) but did win the IRV election. Here are the 9:
SWUNG RACE #1: VIC DIVISION - CORANGAMITE McArthur(lib) was the plurality winner but Cheeseman(Labour) was the IRV winner: name plur-total IRV-total McArthur(liberal) 37438 41260 Cheeseman(labor) 35394 42418 Fiona Nelson(Green) 6319 [We have listed only the top 3 candidates. Fuller data here: http://vtr.aec.gov.au/HouseDivisionFirstPrefs-13745-207.htm] SWUNG RACE #2: NSW DIVISION - BENNELONG name plur-total IRV-total John W Howard(liberal PM!) 38545 41159 Maxine McKew(labor) 38181 43272 Lindsay Peters(Green) 4652 [We have listed only the top 3 candidates. Fuller data here: http://vtr.aec.gov.au/HouseDivisionFirstPrefs-13745-105.htm] SWUNG RACE #3: TAS DIVISION - BRADDON name plur-total IRV-total Mark Baker(liberal) 28307 31231 Sidebottom(labor) 28185 33062 O'Halloran(Green) 5112 [We have listed only the top 3 candidates. Fuller data here: http://vtr.aec.gov.au/HouseDivisionFirstPrefs-13745-193.htm] SWUNG RACE #4: VIC DIVISION - DEAKIN name plur-total IRV-total Barresi(liberal) 33488 36518 Symon(labor) 31732 38727 Pemberton(Green) 6146 [We have listed only the top 3 candidates. Fuller data here: http://vtr.aec.gov.au/HouseDivisionFirstPrefs-13745-193.htm] SWUNG RACE #5: WA DIVISION - HASLUCK name plur-total IRV-total Henry(liberal) 29488 33275 Jackson(labor) 28429 34771 Bremmer(Green) 5706 [We have listed only the top 3 candidates. Fuller data here: http://vtr.aec.gov.au/HouseDivisionFirstPrefs-13745-193.htm] SWUNG RACE #6: NSW DIVISION - PAGE name plur-total IRV-total Gulaptis(nationals) 32480 35912 Safin(labor) 31790 39563 Jongen(Green) 5917 [We have listed only the top 3 candidates. Fuller data here: http://vtr.aec.gov.au/HouseDivisionFirstPrefs-13745-138.htm] SWUNG RACE #7: NSW DIVISION - ROBERTSON name plur-total IRV-total Jim Lloyd(liberal) 36702 40048 Belinda Neal(labor) 34743 40344 Wroblewski(Green) 5600 [We have listed only the top 3 candidates. Fuller data here: http://vtr.aec.gov.au/HouseDivisionFirstPrefs-13745-146.htm] SWUNG RACE #8: NT DIVISION - SOLOMON name plur-total IRV-total David Tollner(CLP) 22495 23882 Damian Hale(labor) 20227 24144 Debbie Hudson(Green) 4308 [We have listed only the top 3 candidates. Fuller data here: http://vtr.aec.gov.au/HouseDivisionFirstPrefs-13745-307.htm] SWUNG RACE #9: TAS DIVISION - BASS name plur-total IRV-total Jodie Campbell(labor) 23764 32553 M.Ferguson(liberal) 27769 31282 Tom Millen(Green) 9745 [We have listed only the top 3 candidates. Fuller data here: http://vtr.aec.gov.au/HouseDivisionFirstPrefs-13745-192.htm]
Since the Australian Election Commission ignored my request for more data (and keeps the full IRV results secret, only distributing simplified election summaries which are not enough information to reconstruct the ballots) we are forced to analyse these elections somewhat simplistically. So let us disregard the other candidates in 4th, 5th, etc place and assume Green voters prefer Labour over NatLib, while Labour voters do not, on average, have an especially noticeable Green-over-Natlib preference, i.e. either would prefer NatLibs or would split about 50-50. (Note: every other party was well behind the Greens so these assumptions are plausibly OK.)
How realistic are those assumptions, and how much does it matter? It is definitely correct that a big majority among Greens prefered Labour over the NatLibs; this is evident both from party stances and more importantly from the elections themselves, which involved many cases where Green vote-transfers made the Labour candidate win. However it is not at all clear that the Labour voters were neutral, or NatLib-favoring, about NatLib versus Green. There is no way to tell how the Labour voters ranked the others from the AEC's simplified election summaries, but we can say that the Labour Party's pre-made "above the line" vote ranked the Greens #2 and the NatLibs second-to-last, which at least suggests Labour voters prefered Greens>NatLibs. We are nevertheless going to proceed under this assumption to see what consequences would follow. Then later, we shall reconsider what happens if we drop this assumption in favor of the opposite view that they prefer Green>NatLib. Actually we shall consider 3 cases: [c1] the Labour voters prefer Green>NatLib, [c2] prefer NatLib>Green, or [c3] do not care. In all 3 cases we will see there had to be a pathology in the election, it is just that we do not always find the same pathology. We shall begin with cases c2 & c3 now, and the "reconsideration" will later handle c1 [which is the one I consider most likely to be actually correct]. We proceed:
[c2 and c3]: All nine of these examples are pathological in the sense that if we add an appropriate number (respectively 30200, 33700, 23100, 26500, 23200, 26200, 30100, 17050, and 15000) of extra Green>Labour>NatLib voters, then those voters, by casting their honest vote, would cause the result to worsen (their most-hated NatLib would win in both cases). In other words we have a "participation failure" or "no-show paradox" or "spoiler" scenario (all 9 examples have the same structure and all 3 of these epithets are simultaneously valid in every case) where adding extra identical honest Green votes would worsen the election winner in the view of these new voters.
These extra Greenies would be better off dishonestly betraying their favorite by ranking him/her below top (IRV doesn't care how far below); they also would be better off not voting (which is in fact what happened). That's the "paradox."
So the picture is fairly clear based on my hopefully-exhaustive examination of all 150 Australian 2007 House races. Exactly two things happened:
If the Labour voters all preferred Green>NatLib, then our analysis above finding "participation failure" pathology in all 9 IRV-swung elections, is invalidated. However, we warn IRV-proponents not to be relieved about that. That's because this new opposed assumption doesn't "save" them so much as "throw them out of the frying pan into the fire."
[c1]: The official pre-made party line vote-recommendations in Australia 2007 were as follows (restricted to Labour,NatLib,Green only and ignoring other parties):
Suppose all the Labour, NatLib, and Green voters indeed voted this way. In that case, Green was the "Condorcet winner," i.e. would have beaten both rivals in a head-to-head contest, in every race in which neither the Labour or NatLib won an outright majority – i.e. in all 9 of the IRV-swung races, plus plausibly a lot more races too.
In all these races, IRV refused to elect that Condorcet winner! The Green candidate would have had the very legitimate gripe "I would have defeated every rival head-to-head, so I should have won"! That's arguably an even worse "pathology" being exhibited by IRV, and whether or not it was "worse," it definitely occurred more often.
The claim that IRV was a "big success" is debatable... and the claim IRV election pathologies are extremely rare is refuted. It is clear that many participation-failure and/or Condorcet-failure pathologies occurred in the 2007 Australian House elections, and in particular apparently in every case where IRV actually mattered, i.e. yielded a different winner than plain-plurality voting.
Range and Approval voting would have outperformed IRV in these elections.
Analogous look at Irish presidential (IRV) elections
Puzzle 55d: the presumed underlying theoretical reason this pathology is so common
IRV "paradox probabilities" calculations in 3 probabilistic models
Return to main page